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\(\left[ \cfrac{\sqrt{2}(2+\sqrt3)}{\sqrt3(\sqrt3+1)}+\cfrac{\sqrt{2}(2-\sqrt3)}{\sqrt3(\sqrt3-1)}\right]\)
\(= \cfrac{\sqrt{2}(2+\sqrt3)(\sqrt3-1)+\sqrt{2}(2-\sqrt3)(\sqrt3+1)}{\sqrt3(\sqrt3+1)(\sqrt3-1)}\)
\(= \cfrac{\sqrt{2}(2\sqrt3-2+3-\sqrt3+2\sqrt3+2-3-\sqrt3)}{\sqrt3(3-1)}\)
\(= \cfrac{\sqrt{2}\times 2\sqrt3}{2\sqrt3}\)
\(= \sqrt{2}\)